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arXiv · 0807.0706

Transfer of Gorenstein dimensions along ring homomorphisms

Lars Winther Christensen·Sean Sather-Wagstaff
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Abstract

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings is to find resolution-free characterizations of the modules for which these invariants are finite. Over local rings, this problem was recently solved for the Gorenstein flat and the Gorenstein projective dimensions; here we give a solution for the Gorenstein injective dimension. Moreover, we establish two formulas for the Gorenstein injective dimension of modules in terms of the depth invariant; they extend formulas for the injective dimension due to Bass and Chouinard.

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Lars Winther Christensen, Sean Sather-Wagstaff. 2009-08-10. Transfer of Gorenstein dimensions along ring homomorphisms. https://arxiv.org/abs/0807.0706

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